Related papers: Kauffman bracket intertwiners and the volume conje…

We study quantum invariant Z(M) for cusped hyperbolic 3-manifold M. We construct this invariant based on oriented ideal triangulation of M by assigning to each tetrahedron the quantum dilogarithm function, which is introduced by Faddeev in…

We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and discuss possible analogues of the affine isoperimetric inequality. In the last…

A key symmetry of classical $p$-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable K\"ahler manifold, we prove that the Lie algebra of…

In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold $K$-theory of an orbifold ${\mathfrak X}$, analogous to the Chen-Ruan orbifold cohomology of ${\mathfrak X}$ in that it uses the obstruction bundle as a quantum…

We study the large $r$ asymptotic behaviour of the Turaev-Viro invariants of oriented Seifert fibered 3-manifolds at the root $q=e^\frac{2\pi i}{r}$. As an application, we prove the volume conjecture for large families of oriented Seifert…

Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…

We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum…

X.-S. Lin and Z. Wang recently made a conjecture concerning the integrality of the Taylor coefficients of the averaged Jones polynomial of algebraically split links. This question is related to a conjectural integrality result for the…

Consider zero-dimensional Donaldson-Thomas invariants of a toric threefold or toric Calabi-Yau fourfold. In the second case, invariants can be defined using a tautological insertion. In both cases, the generating series can be expressed in…

The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the…

Let $\mathbb{P}\Omega^d\mathcal{M}_{0,n}(\kappa)$, where $\kappa=(k_1,\dots,k_n)$, be a stratum of (projectivized) $d$-differentials in genus $0$. We prove a recursive formula which relates the volume of…

Link invariants of long pieces of orbits of a volume-preserving flow can be used to define diffeomorphism invariants of the flow. In this paper, we extend the notions of wrapping number and trunk and define invariants of links with respect…

We construct a new invariant-the trunkenness-for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from the helicity and that it is the limit of a knot invariant…

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1)…

This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various…

The Mahler volume of a centrally symmetric convex body K is defined as M(K)= (Vol K)(Vol K^dual). Mahler conjectured that this volume is minimized when K is a cube. We introduce the bottleneck conjecture, which stipulates that a certain…

Let $(X,\Delta)$ be an $n$-dimensional $\epsilon$-klt log $\QQ$-Fano pair. We give an upper bound for the volume ${\rm Vol}(-(K_X+\Delta))=(-(K_X+\Delta))^n$ when $n=2$ or $n=3$ and $X$ is {$\QQ$-factorial} of $\rho(X)=1$. This bound is…

We construct a new infinite family of ideal triangulations and H-triangulations for the complements of twist knots, using a method originating from Thurston. These triangulations provide a new upper bound for the Matveev complexity of twist…

A new state-sum formula for the evaluation of the Yang-Mills measure in the Kauffman bracket skein algebra of a closed surface is derived. The formula extends the Kauffman bracket to diagrams that lie in surfaces other than the plane. It…

We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume…